Long-range correlations and nonstationarity in the Brazilian stock market

We report an empirical study of the Ibovespa index of the Sao Paulo Stock Exchange in which we detect the existence of long-range correlations. To analyze our data we introduce a rescaled variant of the usual Detrended Fluctuation Analysis that allows us to obtain the Hurst exponent through a one-parameter fitting. We also compute a time-dependent Hurst exponent H(t) using three-year moving time windows. In particular, we find that before the launch of the Collor Plan in 1990 the curve H(t) remains, in general, well above 1/2, while afterwards it stays close to 1/2. We thus argue that the structural reforms set off by the Collor Plan has lead to a more efficient stock market in Brazil. We also suggest that the time dependence of the Ibovespa Hurst exponent could be described in terms of a multifractional Brownian motion.